两元指纹向量聚类问题的复杂性与改进启发式算法

Complexity and Improved Heuristic Algorithms for Binary Fingerprints Clustering

证明丢失值位数不超过2的指纹向量聚类问题为NP-Hard,并给出Figueroa等人指纹向量聚类启发式算法的改进算法.主要改进了算法的实现方法.以链表存储相容顶点集合,并以逐位扫描指纹向量的方法产生相容点集链表,可将产生相容点集的时间复杂性由O(m·n·2p)减小为O(m·(n·p+1)·2p),可使划分一个唯一极大团或最大团的时间复杂性由O(m·p·2p)减小为O(m·2p).实际测试显示,改进算法的空间复杂性平均减少为原算法的49%以下,平均可用原算法20%的时间求解与原算法相同的实例.当丢失值位数超过6时,改进算法几乎总可用不超过原算法11%的时间计算与原算法相同的实例.

This paper proves the binary fingerprints clustering problem for 2 missing values per fingerprint is NP-Hard, and improves the Figueroa＇s heuristic algorithm. The new algorithm improves the implementation method for the original algorithm. Firstly, the linked list is used to store the sets of compatible vertices. The linked list can be produced by scanning the fingerprint vectors bit by bit. Thus the time complexity for producing the sets of compatible vertices is reduced from O（m·n·2^p） to O（m·（n-p＋1）·2^P）, and the the running time of finding a unique maximal clique or a maximal clique is improved from O（m·p·2^pp） to O（m·2^P）. The real testing displays that the improved algorithm takes 49% or lower space complexity of the original algorithm on the average for the computation of the same instance. It can use 20% time of the original algorithm for solving the same instance. Particularly, the new algorithm can almost always use not more than 11% time of the original algorithm to solve the instance with more than 6 missing values per fingerprint.